A parallel beam of red light of wavelength \(700\,\mathrm{nm}\) is incident normally on a diffraction grating that has \(400\) lines per millimetre.
What is the total number of intensity maxima from the grating?
Correct Answer: \( \boxed{\mathrm{B}} \)
The grating spacing is
\(d=\dfrac{1}{400\times10^3}=2.5\times10^{-6}\,\mathrm{m}\).
Using \(d\sin\theta=n\lambda\), the maximum order is
\(n_{\max}=\left\lfloor\dfrac{d}{\lambda}\right\rfloor=\left\lfloor\dfrac{2.5\times10^{-6}}{700\times10^{-9}}\right\rfloor=3\).
Total maxima \(=2n_{\max}+1=2(3)+1=7\).
Therefore, the correct answer is (B).
The equation \(n\lambda=d\sin\theta\) can be used with a diffraction grating to find the wavelength of visible light.
Which quantity is not correct for use in this equation?
| symbol | quantity | |
|---|---|---|
| (A) | \(d\) | distance from grating to screen |
| (B) | \(\lambda\) | wavelength of light |
| (C) | \(n\) | order of intensity maximum |
| (D) | \(\theta\) | diffraction angle of intensity maximum |
Correct Answer: \( \boxed{\mathrm{A}} \)
In the equation \(n\lambda=d\sin\theta\), \(d\) is the spacing between adjacent lines of the diffraction grating, not the distance from the grating to the screen.
The other quantities are correctly defined.
Therefore, the correct answer is (A).
Green laser light passes through a diffraction grating and forms an interference pattern.
The diffraction grating contains \( 400 \) lines per \( \mathrm{mm} \).
The wavelength of the laser light is \( 550\,\mathrm{nm} \).
What is the highest order diffraction maximum produced by the grating?
Correct Answer: \( \boxed{\mathrm{A}} \)
The grating spacing is
\( d=\dfrac{1}{400\times10^{3}}=2.5\times10^{-6}\,\mathrm{m} \).
The highest possible order satisfies
\( n\lambda\le d \).
Hence,
\( n\le\dfrac{2.5\times10^{-6}}{550\times10^{-9}}\approx4.55 \).
The greatest integer value is \( n=4 \).
Therefore, the correct answer is (A).
